Problem: Simplify the following expression: $\dfrac{100n}{40n}$ You can assume $n \neq 0$.
Explanation: $ \dfrac{100n}{40n} = \dfrac{100}{40} \cdot \dfrac{n}{n} $ To simplify $\frac{100}{40}$ , find the greatest common factor (GCD) of $100$ and $40$ $100 = 2 \cdot 2 \cdot 5 \cdot 5$ $40 = 2 \cdot 2 \cdot 2 \cdot 5$ $ \mbox{GCD}(100, 40) = 2 \cdot 2 \cdot 5 = 20 $ $ \dfrac{100}{40} \cdot \dfrac{n}{n} = \dfrac{20 \cdot 5}{20 \cdot 2} \cdot \dfrac{n}{n} $ $\phantom{ \dfrac{100}{40} \cdot \dfrac{1}{1}} = \dfrac{5}{2} \cdot \dfrac{n}{n} $ $ \dfrac{n}{n} = 1 $ $ \dfrac{5}{2} \cdot 1 = \dfrac{5}{2} $